Latest Electromagnetic Theory MCQs – Coordinate Systems and Transforms MCQs ( Electromagnetic Theory ) MCQs
Latest Electromagnetic Theory MCQs
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Electromagnetic Theory MCQs – Coordinate Systems and Transforms MCQs ( Electromagnetic Theory ) MCQs
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Cartesian Coordinate System
1. The Cartesian system is also called as
a) Circular coordinate system
b) Rectangular coordinate system
c) Spherical coordinate system
d) Space coordinate system
Answer: b
Explanation: The other name for Cartesian is rectangular system, which is given by (x,y,z).
2. The volume of a parallelepiped in Cartesian is
a) dV = dx dy dz
b) dV = dx dy
c) dV = dy dz
d) dV = dx dz
Answer: a
Explanation: The volume of a parallelepiped is given by product of differential length, breadth and height.
3. A charge is placed in a square container. The position of the charge with respect to the origin can be found by
a) Spherical system
b) Circular system
c) Cartesian system
d) Space coordinate system
Answer: c
Explanation: Since the container possesses dimensions of a square (length, breadth and height), it can be found by Cartesian system.
4. The scalar factor of Cartesian system is unity. State True/False.
a) True
b) False
Answer: a
Explanation: The range of Cartesian system is one to infinity. Thus the minimum scalar value of the system is unity.
5. The angular separation between the vectors A = 4i + 3j + 5k and B = i – 2j + 2k is (in degrees)
a) 65.8
b) 66.8
c) 67.8
d) 68.8
Answer: c
Explanation: The dot product the vector is 8. Angle of separation is cos θ = 8/ (7.07 X 3) = 0.377 and θ = cos-1(0.377) = 67.8.
6. The Cartesian coordinates can be related to cylindrical coordinates and spherical coordinates. State True/False.
a) True
b) False
Answer: a
Explanation: All the coordinate systems are inter-convertible and all the vector operations are applicable to it.
7. Transform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates
a) -3.6j – 4k
b) -3.6j + 4k
c) 3.6j – 4k
d) 3.6j + 4
Answer: a
Explanation: Convert the Cartesian form to cylindrical form by formula and substitute the points to get -3.6j – 4k.
8. The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by
a) (7,64.62,71.57)
b) (7,-64.62,-71.57)
c) (7,-64.62,71.57)
d) (7,64.62,-71.57)
Answer: d
Explanation: Substitute the points in the vector and convert the Cartesian to cylindrical form to get radius as 7, plane angle1 as 64.62 and plane angle2 as -71.57.
9. Which of the following criteria is used to choose a coordinate system?
a) Distance
b) Intensity
c) Magnitude
d) Geometry
Answer: d
Explanation: The coordinate system is chosen based on the geometry of the given problem. From a point charge +Q, the electric field spreads in all 360 degrees. The calculation of electric field in this case will be spherical system.
10. Vector transformation followed by coordinate point substitution and vice-versa, both given the same result. Choose the best answer.
a) Possible, when the vector is constant
b) Possible, when the vector is variable
c) Possible in all cases
d) Not possible
Answer: a
Explanation: The order of vector transformation and point substitution will not affect the result, only when the vector is a constant.
Cylindrical Coordinate System
1. The cylindrical coordinate system is also referred to as
a) Cartesian system
b) Circular system
c) Spherical system
d) Space system
Answer: b
Explanation: The cylindrical coordinates(r,φ,z) is also called as circular system and is used for systems with circular dimensions.
2. Transform the vector B=yi+(x+z)j located at point (-2,6,3) into cylindrical coordinates.
a) (6.325,-71.57,3)
b) (6.325,71.57,3)
c) (6.325,73.57,3)
d) (6.325,-73.57,3)
Answer: a
Explanation: ρ = √(x2+y2) = √40 = 6.325
Φ = tan-1(y/x) = tan-1(-6/2) = -71.57
z = 3.
3. Cylindrical systems have the following scalar values respectively
a) 1, ρ ,1
b) 1, 1, 1
c) 0,1,0
d) 1,0,0
Answer: a
Explanation: The range of radius is one to unity, that of plane angle is one to 360 degree and that of z plane is one to infinity. Thus the minimum scalar factor has to be 1, ρ , 1.
Vector Analysis And Applications MCQs
4. A charge located at point p (5,30⁰,2) is said to be in which coordinate system?
a) Cartesian system
b) Cylindrical system
c) Spherical system
d) Space system
Answer: b
Explanation: The cylindrical system is of the form (ρ, φ, z), which relates the point given in the question.
5. Cylindrical system is employed in waveguides. State True/False.
a) True
b) False
Answer: a
Explanation: Cylindrical systems are employed in circular waveguides, whereas Cartesian systems are employed in rectangular waveguides.
6. The pressure inside a piston cylinder is a variable of
a) Radius
b) Plane angle
c) Z plane distance
d) Constant, not a variable
Answer: c
Explanation: Pressure varies up and down in a cylinder due to suction. Thus it is dependent on the z plane distance of the cylinder.
7. Charges filled inside a cylindrical will possess flux in which direction?
a) Upwards
b) Downwards
c) Laterally outwards
d) Inwards
Answer: c
Explanation: The flux due to the charges will act outside the cylinder. Since the cylinder possesses curved surfaces, it will flow laterally outwards.
8. Rectangular waveguides dominate the circular waveguides. Find the reason.
a) Low cut-off frequency
b) Easy to design
c) More wave propagation
d) The statement is false
Answer: b
Explanation: Due to linear design, the desired dimensions can be easily constructed using rectangular waveguides than circular ones.
9. Transform the spherical system B = (10/r)i + (10cos θ)j + k into cylindrical form at (5, π/2, -2)
a) 2.467i + j + 1.167k
b) 2.467i – j + 1.167k
c) 2.467i – j – 1.167k
d) 2.467i + j – 1.167k
Answer: a
Explanation: The equivalent cylindrical form is given by,
B = (10sin θ/r + rcos2θ)i + j + (10cos θ/r –r sin θ cos θ)k
At (5, π/2, -2), r = √(52+-22) = √29
sin θ = 5/√29 and cos θ = -2/√29
Thus, B = 2.467i + j + 1.167k.
10. Convert the given rectangular coordinates A(2,3,1) into corresponding cylindrical coordinates
a) (3.21,56.31,1)
b) (3.21,57.31,0)
c) (3.61,57.31,0)
d) (3.61,56.31,1)
Answer: d
Explanation: ρ = √(x2+y2) = √13 = 3.61
Φ = tan-1(y/x) = 56.31
z = 1
Thus, A = (3.61,56.31,1).
Spherical Coordinate System
1. Convert the point (3,4,5) from Cartesian to spherical coordinates
a) (7.07,45⁰,53⁰)
b) (0.707,45⁰,53⁰)
c) (7.07,54⁰,63⁰)
d) (0.707,54⁰,63⁰)
Answer: a
Explanation: r = √(x2+y2+z2) = √50 = 7.07
Θ = cos-1(z/r) = cos-1(5/5√2) = 45⁰
Φ = tan-1(y/x) = tan-1(4/3) = 53⁰.
2. Example of spherical system in the following is
a) Charge in space
b) Charge in box
c) Charge in dielectric
d) Uncharged system
Answer: a
Explanation: From a point charge +Q, the electric field spreads in all 360 degrees. The calculation of electric field in this case will be spherical system. Thus it is charge in the space.
3. Spherical systems are employed in waveguides. State True/False
a) True
b) False
Answer: b
Explanation: There is no waveguide designed spherically to avoid absorption, rather than propagation.
4. Choose which of following condition is not required for a waveguide to exist.
a) The dimensions should be in accordance with desired frequency
b) Cut-off frequency should be minimum 6GHz
c) The shape should be spherical
d) No specific condition is required for waveguide design
Answer: c
Explanation: A waveguide need not be spherical, it has to be rectangular or circular, as it violates the propagation of the wave.
5. Find the spherical coordinates of A(2,3,-1)
a) (3.74, 105.5⁰, 56.13⁰)
b) (3.74, 105.5⁰, 56.31⁰)
c) (3.74, 106.5⁰, 56.13⁰)
d) (3.74, 106.5⁰, 56.31⁰)
Answer: b
Explanation: r = √(x2+y2+z2) = √14 = 3.74
Θ = cos-1(z/r) = cos-1(-1/3.74) = 105.5⁰
Φ = tan-1(y/x) = tan-1(3/2) = 56.31⁰.
6. Find the Cartesian coordinates of B(4,25⁰,120⁰)
a) (0.845, 1.462, 3.625)
b) (-0.845, 1.462, 3.625)
c) (-8.45, 2.462, 6.325)
d) (8.45, 2.462, 6.325)
Answer: b
Explanation: x = r sin θ cos φ = 4 sin25⁰ cos 120⁰ = -0.845
y = r sin θ sin φ = 4 sin 25⁰ sin 120⁰ = 1.462
z = r cos θ = 4 cos 25⁰ = 3.625.
7. The area of sphere can be computed from the sphere volume. State True/False.
a) True
b) False
Answer: a
Explanation: On double integrating the differential volume, the area can be computed for a sphere.
8. Given B= (10/r)i+( rcos θ) j+k in spherical coordinates. Find Cartesian points at (-3,4,0)
a) -2i + j
b) 2i + k
c) i + 2j
d) –i – 2k
Answer: a
Explanation: r = √(x2+y2+z2) = √25 = 5
Θ = cos-1(z/r) = 1
Φ = tan-1(y/x) = tan-1(-4/3)
Thus, B = -2i + j.
9. The scalar factor of spherical coordinates is
a) 1, r, r sin θ
b) 1, r, r
c) r, r, 1
d) r, 1, r
Answer: a
Explanation: The radius varies from unity to infinity, the plane angle from zero to 360 ⁰ and the z plane from (-∞, ∞) .
10. Transform the vector (4,-2,-4) at (1,2,3) into spherical coordinates.
a) 3.197i – 2.393j + 4.472k
b) -3.197i + 2.393j – 4.472k
c) 3.197i + 2.393j + 4.472k
d) -3.197i – 2.393j – 4.472k
Answer: b
Explanation: r = √(x2+y2+z2) = 3.74
Θ = cos-1(z/r) = cos-1(3/3.74) = 36.7⁰
Φ = tan-1(y/x) = tan-1(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j + (-4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.